The issue with the phone number is in the pattern attribute on the <input> field. The formatting is done in the onblur event. You could remove or adjust both to allow more digits and stop formatting the entered value.
The continue button is there because when the wizard runs, usually the payment info div isn't visible. The continue button would refresh the cart in case the shipping had changed and expose the payment div.
Something you have done has made the payment div show by default and made the continue button not make sense.
I think the problem stems from you not having uploaded some of the necessary scripts.. Try uploading the webassist and WA_eCart directories. They both have .js and .css files that the page uses that aren't on your server. I can see there are actually 13 files referenced on your page that don't currently exist on your server.